Deconstruction of a Dirichlet–Nazimow formula

Dirichlet (J Reine Angew Math 24, 1842 ) announced a generalization of his class number formula for real quadratic fields to biquadratic fields containing , by replacing the circular trigonometric functions with certain elliptic trigonometric functions. Subsequently, Nazimow (Ann Sci École Norm Sup...

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Bibliographic Details
Published in:Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2011-03, Vol.105 (1), p.109-117
Main Authors: Gómez-Molleda, Mariángeles, Lario, Joan-C.
Format: Article
Language:English
Subjects:
Algebra
Applications of Mathematics
Dirichlet problem
Field theory
Fields (mathematics)
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Norms
Number theory
Original Paper
Proving
Theoretical
Trigonometric functions
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Summary:Dirichlet (J Reine Angew Math 24, 1842 ) announced a generalization of his class number formula for real quadratic fields to biquadratic fields containing , by replacing the circular trigonometric functions with certain elliptic trigonometric functions. Subsequently, Nazimow (Ann Sci École Norm Sup (3) 5:147–176, 1888 ) published the corresponding formula. Here we analyze the Dirichlet–Nazimow formula and update its proof in the context of Class Field Theory.
ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-011-0013-y